Washington (CNN) - Just one day after President Donald Trump dismissed national security adviser John Bolton, administration officials are discussing the possibility of replacing Bolton with his chief rival, Secretary of State Mike Pompeo. Under this scenario, the country's top diplomat would absorb the national security adviser role and do both jobs, according to a senior administration official and a source familiar with the possibilities.

That would make Pompeo the second person in history to have both jobs at the same time. The first, Henry Kissinger, was already President Richard Nixon's national security adviser when he was appointed secretary of state in 1973, and filled both roles for two years.

It's unclear how seriously Trump is considering this possibility, and a source familiar with the process says that Pompeo has given the President a list of other names to consider. On Wednesday, when asked about his top picks to replace Bolton, the President said, "I have five people that want it very much... Five people that I consider very highly qualified, good people."

Tuesday night, attending a Washington charity ball with his wife, Pompeo laughed with friends about Bolton being fired. The two were often at odds with each other and had even stopped talking to each other outside formal meetings. Pompeo was jovial and his mentality was "what a day, what a life, what a job," explained a source who was at the event.

For now, Pompeo will remain the President's primary foreign policy adviser, explained another source close to the White House.

"He is going to act as national security adviser at least in the near term. Trump is happy with that," the person said.

An administration official cautions that "the Kissinger model" could be dangerous for Pompeo, especially given his dominant position within the administration. With a dual role, Pompeo risks becoming too powerful for Trump's taste, the source said.

Counselor to the President Kellyanne Conway didn't discount the possibility on Thursday, calling him an "excellent" secretary of state who "has the President's ear" and noted that it would not be unprecedented, pointing to Kissinger. She did say that Trump is looking "at a slate of about five or so" options, with Pompeo making that list "five-plus."

The Washington Examiner was first to report the idea is being discussed.

The White House and State Department did not respond to requests for comment.

Other possibilities

If Trump opts to keep the position as a stand-alone role, nearly a dozen potential Bolton successors are being floated.

A senior administration official and source with knowledge of the matter told CNN on Wednesday that as of now, Brian Hook, the US special representative for Iran and senior policy adviser to Pompeo at the State Department and Steve Biegun, the special envoy to North Korea, have emerged as top contenders.

While sources have cautioned that Trump could always change his mind and pick a candidate who is not currently being discussed, Hook or Biegun would be a marked departure from Bolton.

Unlike Bolton, who was criticized by Trump on Wednesday for his positions on several foreign policy issues, including Iran and North Korea, Hook and Biegun are unlikely to challenge the President's desire for diplomatic deal-making, a quality that appears to be a prerequisite for the national security adviser post.

Some officials said this week that Bolton's acrimonious departure was a sign that the role he occupied could be diminished going forward. Much like Trump acts as his own communications director and chief of staff — despite having actual staff members in those roles — he is likely to look warily on another national security adviser who acts with as much leeway as Bolton did.

Eager to rack up wins ahead of next year's reelection battle, Trump will also weigh a new adviser's political savvy, particularly as he looks to fulfill campaign promises like withdrawing troops from Afghanistan and securing diplomatic deals.

The problem, officials and analysts say, is that like with most elements of his agenda, Trump's views on foreign policy are ever-changing. When Bolton entered his post 17 months ago, Trump was agitating to withdraw from the nuclear deal with Iran, frustrated with the coterie of advisers who were urging him to remain in the accord.

Now, after applying maximum pressure to Iran's regime, hitting the country and its leaders with heavy-handed sanctions, Trump is turning in the other direction and looking for a diplomatic opening. With Bolton -- who argued against diplomacy -- now gone, Trump is entertaining the possibility of meeting Iranian President Hassan Rouhani at the United Nations later this month.

Those differences — paired with Bolton's isolation among Trump's other advisers — were his downfall.

"I hope we've left in good stead, but maybe we have and maybe we haven't," Trump said — a nod to the emerging discrepancies in how and when Bolton left his administration post.

Trump went on to criticize Bolton for almost upending North Korea talks with his reference to the "Libya model," his advocacy for the Iraq War during his tenure in the George W. Bush administration and his views toward Venezuela.

"He made some very big mistakes," Trump said of his freshly departed adviser. "He wasn't getting along with people in the administration that I consider very important."

Regardless of who, if anyone, replaces Bolton, Trump made it clear Wednesday that he will be the one calling the shots on US foreign policy and possibly changing course.